If the sum of the zeros of the quadratic polynomial

Question:

If the sum of the zeros of the quadratic polynomial $k x^{2}+2 x+3 k$ is equal to the product of its zeros, then $k=?$

(a) $\frac{1}{3}$

(b) $\frac{-1}{3}$

(c) $\frac{2}{3}$

(d) $\frac{-2}{3}$

Solution:

(d) $\frac{-2}{3}$

Let $\alpha$ and $\beta$ be the zeroes of $k x^{2}+2 x+3 k$.

Then $\alpha+\beta=\frac{-2}{k}$ and $\alpha \beta=\frac{3 k}{k}=3$

$=>\alpha+\beta=\alpha \beta$

$=>\frac{-2}{k}=3$

$=>k=\frac{-2}{3}$

 

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